Challenge Quizzes

Total displacement from velocity vectors

A rocket initially at (0,0)(0,0)(0,0) moves with a constant velocity of (7 m/s,6 m/s)(7\text{ m/s},6\text{ m/s})(7 m/s,6 m/s) through vacuum. After moving for 54 s,54\text{ s},54 s, an asteroid hits the rocket and a change of (1 m/s,0)(1\text{ m/s},0)(1 m/s,0) is made to the rocket's velocity. What is the position vector of the rocket at t=60 s?t=60\text{ s}?t=60 s?

A man initially at (0,0)(0,0)(0,0) on the coordinate plane walks with a velocity of (3 m/s,−5 m/s)(3\text{ m/s},-\sqrt{5}\text{ m/s})(3 m/s,−5​ m/s) for 222 seconds. Then he walks with a velocity of (−1 m/s,1 m/s)(-1\text{ m/s}, 1\text{ m/s})(−1 m/s,1 m/s) for 333 seconds. Find the magnitude of his total displacement.

You wish to swim across a small river to your friend on the other side. The river is 30 meters wide and you begin to swim straight across it at a speed of 1 m/s. The current in the river is 0.5 m/s and so the river carries you downriver as you swim. How far downriver in meters are you when you get to the other side?

A train is moving at a constant speed of 80 km/h.80\text{ km/h}.80 km/h. The train first moves in the +x+x+x direction for an hour. Then it turns 60∘60^{\circ}60∘ upward and moves for two hours. Find the magnitude of the train's total displacement.